The Trompeta Bastarda was a Spanish Trumpet
with half-length resonators, as opposed to the
Trompeta Real which had
full-length resonators.
Like many Spanish reeds, the Trompeta Bastarda was often mounted
en chamade.
The Spanish word bastarda means a piece of ordnance (i.e. a cannon).

Trompeta Recordata is mentioned only by Maclean, who describes it
only as an 8' Trumpet with half-length resonators.
Without further
information, we assume it to be synonymous with Trompeta Bastarda.
Its etymology is not known.
Contributions welcome.

Trompeta Bastarda 8', Organo de Eco (left); Santa María la Real,
Xunqueira de Ambía, Orense, Spain; Valdonado 1759. This example has
ceramic resonators, as can be seen in the photo below (reproduced courtesy
of Rick Berg).
While Osiris lists it at 8', a different source lists it at 4',
though this may have been based on the resonator length rather than
the speaking pitch.